EARTH AS A SPHERE

LATITUDE AND LONGITUDE The coordinate system that we use to

locate places on Earth is the terrestrial system. The coordinates in the terrestrial system are Latitude and Longitude.

e.g: Kuala Lumpur ( 3 8’ N , 10142’ E )

LONGITUDE Longitude, denoted symbolically by the

Greek letter Lambda, is divided in meridians (not parallel to each other, they converge at the poles), which are measured in degrees East or West of the Prime Meridian, also known as Greenwich Meridian The Prime Meridian serves as a starting point for the measurement of degrees in either East or West directions. It marks longitude 0°.

LONGITUDE

LONGITUDEThe Prime Meridian is the meridian (line of longitude) at which the longitude is defined to be 0°.The Prime Meridian and its opposite the 180th meridian (at 180° longitude), which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.

LONGITUDE

LONGITUDE Another meridian of great importance is

the Dateline Merdian, which marks longitude 180° (either E or W). This meridian is the exact oposite of the Prime Meridian on the globe. 

LONGITUDEMeridian- is one half of a great circle joining the

North and South Poles.

Longitude of a meridian- is determined by the angle between its

plane and the plane for GM , either to the east or to the west of the GM.

LONGITUDE

150 E

LONGITUDEMeridians that are opposite to each other and form a great circle, have longitudes x E and ( 180 – x) W or x W and (180-x) E

- Great circle is a circle with centre at the centre of the Earth.

Longitude

The Difference between Two Longitudes

If longitudes X and Y are on the same side of the GM, then the difference between X and Y is ( X – Y).

If the longitudes X and Y are on the different sides of the GM , then the difference between X and Y is ( X + Y )

Longitude

LATITUDE

LATITUDE Parallels of latitude are circles on the surface of

the Earth, parallel to the equator and labeled according to their angular distance from the equator.

Parallel of latitudes is NOT a great circle !

LATITUDE Latitude is the angle

subtended by a meridian at the centre of the earth beginning from the equator to the parallel of latitude which is either to the North or to the South of the Equator.

LATITUDE

LATITUDE DIFFERENCE BETWEEN TWO

LATITUDES - If latitudes X and Y are on the same side of

the Equator, then the difference between X and Y is ( X – Y).

If the latitudes X and Y are on the different sides of the Equator , then the difference between X and Y is ( X + Y )

LATITUDE

Calculate the difference between the latitudes below i. Latitudes 70N and 64N

ii. Latitudes 64N and 55S

LOCATION OF A PLACEThe location of a place is determined by its latitude and longitude. Based on the diagram state the location s of A , B ,C , D and E

LOCATION OF A PLACE

DISTANCE ON THE SURFACE OF THE EARTH.

The distance between two places on the surface of the Earth is measured in nautical miles.

1 is equal to 60 nautical miles. Any two points on a sphere is always

connected by a circular path. The shortest distance between two

points is the distance taken along the great circle.

BIG FAT LIE!

DISTANCE BETWEEN TWO POINTS ALONG THE MERIDIAN

Distance of two points on the surface of the Earth measured along the meridian ( same longitude, different latitude) is given by= ( the difference in latitude X 60’ )= ( 60’ )

DISTANCE BETWEEN TWO POINTS ALONG THE MERIDIAN

Given that P(60N,30 W) and Q ( 40 S , 30W) , find the distance of PQ measured along the meridian.

Answer:Distance = ( 60 + 40 ) 60’ = 100 x 60’ = 6000 nautical miles.

DISTANCE BETWEEN TWO POINTS ALONG THE MERIDIAN

In the diagram , A ( 45N , 30E) and B are two points on the surface of the earth. Given that the distance between A and B is 4800 nm measured along the longitude 30E . Find the location of B

DISTANCE ALONG THE EQUATOR

The distance between points P and Q on the Equator ( same latitude, different longitude) is equivalent to the angle at the centre of the earth POQ, in minutes.

= (difference in longitude ) x 60’

DISTANCE ALONG THE EQUATOR Example: Given that P( 0, 124W) , Q (0, 72W)

and R( 0, 27 E ). Calculate the distance between

i. P and Q ii. Q and R

DISTANCE ALONG THE EQUATOR Example; Given that P(0, 160W) and the

distance between P and Q measured along the Equator is 5400 n.m. Find all the possible locations of Q.

Relation Between Radius of the Earth and Radius of a Parallel of Latitude

OP = OQ = RAQ is parallel to OPPOQ = OQA ( alternate angle of two parallel lines)By trigonometric ratio ,

Cos =

Therefore, r = R Cos

Rr

Rr

Relation between the Lengths of Arcs on the Equator and Parallels of Latitude

-Let r be the radius of the parallel of latitude and R be the radius of the Equator.

-Then , the circumference of the parallel latitude is 2r and the circumference of the Equator is 2R

Relation between lengths of Arc on the Equator and parallels of latitude

Distance along the parallel of latitudeDistance of PQ = MN (Cos ) = MON 60 Cos = Diff. in long of PQ 60 Cos(lat of PQ)

eg: Find the distance between P( 60N, 35W) and Q( 60N, 45 E).

Find the distance between P( 60N, 35W) and Q( 60N, 45 E).

//Dist. of PQ = (diff. in longitude) 60’ Cos

= (35 + 45 ) 60 Cos 60 = 2400’ Distance of PQ = 2400 n.m

SHORTEST DISTANCE BETWEEN TWO POINTS The shortest distance between two

points on the surface of the Earth is the arc on the great circle that passes through the two points.

The Equator and all circles passing through the North and South Poles are great circles.

SHORTEST DISTANCE

a. Along the meridian ( same longitude )

b. Along the Equator

SHORTEST DISTANCEDistance of two points that passing through the North/South Poles* P and Q are on the same great circle*The difference in longitudes = 180

•The shortest distance of PQ= ( POQ = ) x 60’= ( 180 - lat P – lat Q) 60’

Shortest Distance Calculate the shortest distance between

P ( 48N, 45E) and Q( 53N, 135W).

= 180

PQ ( shortest distance through North pole) = (180 – 48 – 53) x 60’ = 4740’ = 4740 n.m